Sen. John McCain, who has been sharply critical of UN Ambassador Susan Rice for consideration as secretary of state, Sunday appeared to soften his opposition.

"I think she deserves the ability and the opportunity to explain herself and her positions," McCain (R-Ariz.) said in an interview on "Fox News Sunday."

As McCain's stance appeared to change, so did another critic, Sen. Lindsey Graham (R-S.C.). Graham also said Rice should be given the opportunity to explain her positions. Instead of repeating his earlier assertion that he was "dead set" against a Rice promotion, Graham suggested on ABC's "This Week" that he looked forward to hearing her out.

However, Rep. Peter King (R-Seaford) remained highly critical. He said Sunday in a "Meet the Press" interview that Rice should have more thoroughly studied top-secret intelligence available to her about the Sept. 11 attack in Benghazi, Libya, rather than act as a "puppet."

Rice should not have portrayed the deadly assault on the U.S. Consulate in Benghazi as a spontaneous response to an anti-Muslim YouTube video when it was a terrorist attack, King said, reiterating a stance taken by many other Republicans. The attack killed the U.S. ambassador to Libya and three other Americans.

"If she's sent out there to speak to the American people about what happened in Benghazi, she's obligated to do more than look at three sentences of unclassified, or five sentences of unclassified talking points, because that was basically a cover story," said King, chairman of the House Homeland Security Committee.

Rice, in a news conference Wednesday, said she had been asked to speak about the Benghazi attack on Sunday talk shows Sept. 16 and "relied solely and squarely on information provided to me by the intelligence community." She said she had presented the information as preliminary.

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King told Newsday Sunday that Rice "has done a good job at the UN" representing the United States, but on Sept. 16 she "could have said, without compromising anything, . . . that we're looking at a number of possible causes, including the video, including terrorist involvement, but it'll be a number of days until we come to a conclusion."